Fast super-resolution algorithm using rotation-invariant ELBP classifier and hierarchical pattern matching

This paper proposes a fast super-resolution (SR) algorithm using content-adaptive two-dimensional (2D) finite impulse response (FIR) filters based on a rotation-invariant classifier. The proposed algorithm consists of a learning stage and an inference stage. In the learning stage, we cluster a sufficient number of low-resolution (LR) and high-resolution (HR) patch pairs into a specific number of groups using the rotation-invariant classifier, and choose a specific number of dominant clusters. Then, we compute the optimal 2D FIR filter(s) to synthesize a high-quality HR patch from an LR patch per cluster, and finally store the patch-adaptive 2D FIR filters in a dictionary. Also, we present a smart hierarchical addressing method for effective dictionary exploration in the inference stage. In the inference stage, the ELBP of each input LR patch is extracted in the same way as the learning stage, and the best matched FIR filter(s) to the input LR patch is found from the dictionary by the hierarchical addressing. Finally, we synthesize the HR patch by using the optimal 2D FIR filter. The experimental results show that the proposed algorithm produces better HR images than the existing SR methods, while providing fast running time.     

Up-scaling Flow in Fractured Media: Equivalence Between the Large Scale Averaging Theory and the Continuous Time Random Walk Method

In a recent paper, (McNabb, 1978), we set up a method allowing to compute both the transient and steady-state exchange terms between the matrix and fractured regions of a naturally fractured porous medium using the continuous time random walk method (CTRW). In particular, the exchange coefficient parametrizing the large-scale exchange term was computed on physical grounds using a time integration of the so-called time correlation function corresponding to the particle presence in the fractures. On the other hand, the large scale averaging theory (LSAT) as developed by Quintard and Whitaker (Quintard and Whitaker, 1996) gives another definition for this exchange coefficient . It also provides a so-called closure problem allowing to compute from the solution of a well-defined steady state boundary value problem, to be solved over a representative volume of the high resolution fractured map. The goal of the present paper is to show analytically that both definitions coincide, yielding a unique and well defined value of the coefficient. This provides an unification of two approaches whose respective backgrounds are very different at the first glance.     

Permeability up-scaling using Haar Wavelets

In the context of flow in porous media, up-scaling is the coarsening of a geological model and it is at the core of water resources research and reservoir simulation. An ideal up-scaling procedure preserves heterogeneities at different length-scales but reduces the computational costs required by dynamic simulations. A number of up-scaling procedures have been proposed. We present a block renormalization algorithm using Haar wavelets which provide a representation of data based on averages and fluctuations. In this work, absolute permeability will be discussed for single-phase incompressible creeping flow in the Darcy regime, leading to a finite difference diffusion type equation for pressure. By transforming the terms in the flow equation, given by Darcy’s law, and assuming that the change in scale does not imply a change in governing physical principles, a new equation is obtained, identical in form to the original. Haar wavelets allow us to relate the pressures to their averages and apply the transformation to the entire equation, exploiting their orthonormal property, thus providing values for the coarse permeabilities. Focusing on the mean-field approximation leads to an up-scaling where the solution to the coarse scale problem well approximates the averaged fine scale pressure profile.     

Image super-resolution by curve fitting in the threshold decomposition domain

A new curve-fitting scheme is proposed in this paper to produce super-resolution images from a single low-resolution source image. The most unique feature of this method is that the threshold decomposition is performed on the given source image to obtain multiple binary images so that the curve-fitting applied on each resulted binary image can be made very efficient and accurate, thus allowing us to focus on tiny objects and thin structures so as to achieve rather nice visual results even when a large up-scaling factor is used. Two novel techniques are further proposed to improve the visual quality: (1) a spreading technique (applied on some significant pixels detected in each threshold decomposed binary image) is used to remove ladder-like false edges that often appear visually in super-resolution images, and (2) an edge correction (guided by the edge information extracted from the original source image) is used to sharpen all inherent edges. Our results are compared with those achieved by using the state-of-arts techniques, showing the ability of our algorithm to achieve a better visual quality in smooth areas as well as for sharp edges and small objects.     

Two-Phase Inertial Flow in Homogeneous Porous Media: A Theoretical Derivation of a Macroscopic Model

The purpose of this article is to derive a macroscopic model for a certain class of inertial two-phase, incompressible, Newtonian fluid flow through homogenous porous media. Starting from the continuity and Navier–Stokes equations in each phase β and γ, the method of volume averaging is employed subjected to constraints that are explicitly provided to obtain the macroscopic mass and momentum balance equations. These constraints are on the length- and time-scales, as well as, on some quantities involving capillary, Weber and Reynolds numbers that define the class of two-phase flow under consideration. The resulting macroscopic momentum equation relates the phase-averaged pressure gradient to the filtration or Darcy velocity in a coupled nonlinear form explicitly given by